There is a strong need to reduce the switching voltage, or Vπ, of electro-optic modulators used in optical communication systems. Electro-optic modulators with reduced switching voltages have increased conversion efficiency and do not require high power driver stages at the modulator input. This disclosure presents a modulator structure that directly benefits narrowband optical subcarrier systems, where only a fraction of the available modulator bandwidth is utilized about a center frequency. One such application is the optical distribution of radio signals. The potential of these systems is expanding, particularly for distributing signals in local multipoint distribution systems (LMDS's) which deliver broadband data services over a wireless link to the home. The switching voltage of the modulator has a significant impact on the performance of these distributions systems, particularly with respect to the link loss between the transmitter and receiver. High switching voltages lead to very high link loss, even over insignificant lengths of fiber, with typical losses being 25-50 dB for modern optical intensity modulators. Another application is optical pulse generators, where electro-optic modulators are driven by sinusoidal signals and their nonlinear nature is exploited to generate narrow optical gating functions. This application also benefits from devices with low switching voltages since the drive requirements for such systems are very demanding.
One of the most common realizations of an electro-optic modulator is an optical phase modulator, shown in FIG. 1. This modulator consists of an optical waveguide 10 with an optical input 6 and an optical output 8, formed from an electro-optic material and an electrode structure 12 that develops an electric field across the waveguide 10 in accordance with an electrical signal applied to the electrode 12 from the signal input 5. The electric field changes the refractive index of the electro-optic material in a linear fashion so that the phase imparted to the outgoing optical wave is directly proportional to the applied electrical signal. Phase modulation of the optical wave can in turn be used for the transmission of information in an optical communication system, most commonly through the use of Mach-Zehnder interferometers which use multiple optical phase modulators to achieve intensity and/or phase modulation of an optical wave.
In traditional modulator structures, the electrode 12 is terminated in an impedance 14 matched to the characteristic impedance of the electrode 12 so that the applied electrical signal travels along the length of the electrode 12 and is fully absorbed by the termination 14. Such an electrode structure 12 is known as a traveling-wave electrode. If the velocities of the electrical signal propagating along the electrode and the optical wave traveling in the electro-optic material are matched, this structure yields a very high modulation bandwidth. However, this structure is not optimally suited for narrowband applications because the broadband nature of the modulator is achieved in exchange for a relatively high switching voltage. The main reason for this is that most of the power in the electrical signal applied to the electrode 12 is dissipated in the termination 14, leading to relatively small electric fields being established across the optical waveguide 10. This in turn, yields a weak electro-optic effect, increasing the switching voltage of the device, and necessitating the use of high power amplifier stages at the input to the modulator in order to achieve the desired modulation depth.
This situation can be improved significantly by employing resonant modulator electrodes, which reduce the switching voltage of an electro-optic modulator over a narrow frequency band. In such structures, such as the one shown in FIG. 2, the termination at the end of the modulator electrode 12 is removed and replaced with an electrical reflector 16 such as an open or a short, and a coupler 18 is introduced between the signal input 5 and the input to the electrode 12 so that the electrode 12 is transformed into a resonator The electrically sensitive, or active, region 17 of the modulator has a length L. The active region may be surrounded by sections of electrode 12 that do not influence the optical wave traveling in the waveguide, marked as passive regions 20 in the diagram. The output of the electrode 12 is connected to the electrical reflector 16, having a reflection coefficient ΓL, while the input of the electrode is connected to the coupler 18 which couples electromagnetic energy into the resonator It has a reflection coefficient ΓC.
The arrangement of the reflector 16 and the coupler 18 traps microwave energy inside the resonator. Waves that are admitted into the resonator travel forward towards the reflector 16, where they are reflected. The reverse-traveling waves travel back towards the coupler 18, where they are re-reflected into the resonator. This continual feedback process establishes many forward- and reverse-traveling waves within the resonator. Over a small frequency range, the superposition of these waves yields a standing wave within the resonator. The coupler 18, realized, for instance, with a reactive component such as a series capacitor or shunt inductor, is chosen so that the resonator is critically coupled. Under this condition, a conjugate match exists between the source and the resonator, resulting in maximum energy transfer between the drive circuitry and the resonator. This resulting standing wave in the resonator has a very large amplitude relative to the applied signal, leading to much greater fields being established across the active region of the modulator than can be achieved with a standard traveling-wave structure. This reduces the switching voltage of the modulator considerably. Resonant electrode structures have been investigated in the literature quite extensively; see G. K. Gopalakrishnan and W. K. Bums, “Performance and Modeling of Resonantly Enhanced LiNbO3 Modulators for Low-Loss Analog Fiber-Optic Links”, IEEE Transactions on Microwave Theory and Techniques, vol. 42, no. 12, pp. 2650-2656, December 1994, Y. S. Visagathilagar, A. Mitchell, and R. B. Waterhouse, “Fabry-Perot Type Resonantly Enhanced Mach-Zehnder Modulator ”, MWP'99 Digest, pp. 17-20, 1999.
The resonator arrangement shown in FIG. 2 is known as a linear resonator. Alternatively, a resonator can be formed by forming the resonant element into a loop to form a ring resonator, as shown in FIG. 3, with signal input 5, where part of the transmission line composing the ring is coupled through coupler 24 to the active section 17 of the modulator, again surrounded with possible passive regions 20. Regardless of the implementation, the net result is the establishment of a standing wave across the active region of the modulator which improves the response of the modulator at specific frequencies. Resonant modulators have been explored in a number of patents; see G. K. Gopalakrishnan, “Optical modulator for CATV Systems”, U.S. Pat. No. 5,787,211, 1998. The fields in a resonant structure can also be applied using microwave waveguides instead of planar structures, as in A. A. Godil, “Partially Loaded Microwave Waveguide Resonant Standing Wave Electro-Optic Modulator”, U.S. Pat. No. 5,414,552, 1995.
Resonant modulators work by sacrificing the bandwidth of a traveling-wave modulator for a reduced switching voltage over a specific frequency band. Since the systems being considered here are inherently narrowband, this tradeoff is inconsequential. However, there are several issues that limit the performance of resonant modulators. First, the upper frequency at which a resonant modulator can operate is constrained by the resonator length. Although any number of wavelengths can be established inside the microwave resonant circuit, for maximum modulator response, the resonator length must be chosen so that approximately half the wavelength associated with the target frequency to be used with the device is established across the active region of the device (i.e. L=λ/2, where λ is the wavelength of the electrical signal at resonance). At high frequencies, this requires that the active region of the modulator be very short. However, shortening the interaction length of the modulator increases the overall switching voltage of the device and can reduce or nullify the improvements introduced by resonant enhancement. Keeping the interaction length constant and utilizing higher order resonator modes results in a degraded response compared to the case when a half-wavelength field profile is developed over the active region length. Hence, it would be desirable if the interaction length of the device could be kept constant at a specific length to yield a given switching voltage while eliminating the constraint that a half-wavelength be developed across the interaction length of the modulator at the desired resonant frequency.
Second, since it takes an optical wave a finite amount of time to traverse the active region of an electro-optic modulator, transit time effects limit the amount of enhancement offered by a resonant modulator, especially at very high frequencies. These effects are present because fundamentally a resonant electrode cannot be velocity-matched to the optical wave because the standing wave established across the resonant electrode is a superposition of forward- and reverse-traveling waves. The reduction in modulator response caused by this effect is well documented in, for example, L. A. Molter-Orr, H. A. Haus, and F. J. Leonberger, “20 GHz Optical Waveguide Sampler”, IEEE Journal of Quantum Electronics, vol. QE-19, pp. 1877-1883, December 1983.
Given these constraints, it is an object of the present invention to achieve the following:                1. Provide an electrode structure offering all the advantages of traditional resonant electrode structures, while possessing an arbitrary interaction length. That is, the interaction length of this modulator is not constrained to be λ/2 at the desired resonant frequency of the device. Arbitrary interaction lengths also enable the resonant frequency of the device to be variable.        2. Provide an electrode structure that is immune to, or substantially less affected by, optical transit time effects that limit the performance of traditional resonant electrode structures.        
Traditional resonant modulators develop a standing wave electric field pattern across the active region of the modulator. While the amplitude of the standing wave is much larger than that achievable with traveling-wave modulators, the length of the active region cannot exceed λ/2, otherwise the additional modulation depth achieved by the resonant electrode configuration will be lost.